The agreement was used to export weapons to the kingdom, which is leading a coalition in a controversial bombing campaign in Yemen.
The former business secretary said he was given assurances the UK would be granted oversight over where British-made weapons were used. Such a level of control was afforded to the Americans.
Sir Vince says these promises assured him the risk to innocent lives was minimal and led him to sign licences for laser-guided Paveway IV weapons.
Since the Yemen conflict escalated in March 2015 - when the Saudi-led coalition started its campaign in support of the Yemeni government and against Houthi rebels - at least 11,000 civilians have been killed.
The MoD has denied military personnel were involved in the “targeting chain” and denied the assurances were ever offered to Sir Vince.
"That is categorically contrary to what I was told was going to happen,” Sir Vince told The Guardian.
“If what they are now saying [is] I was not offered oversight on an equivalent level to the Americans, and that this would involve oversight of targeting, then I was seriously misled.
“That is total fabrication because that was very specifically stated. That is not something that I would have made up."
He added: "My very clear understanding was that the equipment would be supplied to Saudi Arabia on the very clear basis that British personnel would have oversight of what the Saudi air force was doing, on the same basis as the Americans."
Sources told the newspaper the MoD was "desperate" to get the licences signed off because the Saudis were putting "enormous pressure" on the Government.
More than three million people have been displaced by the conflict in Yemen and at least 80 per cent of the population now relies on humanitarian aid, according to Human Rights Watch.
Fourteen million people in the country are hungry and 370,000 children are starving, due to the Saudi-led bombardment of the country an a blockade against food imports, Unicef has said.
Shadow foreign secretary Emily Thornberry said: "It is extremely disturbing to discover that the sale of arms for use in Yemen was approved by Vince Cable on the basis of a lie, and provides yet more evidence that limiting civilian casualties in this conflict has been the least of the Government's concerns".
The MoD told The Guardian while it had agreed to "increase oversight of the targeting process" last year, this did not never included oversight of precisely where air strikes were carried out.
"British personnel are not involved in carrying out strikes, directing or conducting operations in Yemen or selecting targets and are not involved in the Saudi targeting decision-making process," a spokesman said.
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